Question

If five times the fifth term of an A.P is equal to eight times it eighth term, show
that the 13th term is zero.

Answer 1

Answer:

given: 5×t5=8×t8

5×(a+4d)=8×(a+7d)

5a+20d=8a+56d

8a-5a=56d-20d

3a=-36d

a= -12d. .....1

to prove:t13=0

proof:

a+12d

-12d+12d=0 (from 1)

hence proved

Answer 2

Step-by-step explanation:

5th term= a+4d

8th term= a+7d

According to the question,

5(a+4d) = 8(a+7d)

5a+20d = 8a+56d

5a-8a = 56d-20d

-3a = 36d

Dividing by 3, we have,

-a = 12d

a+12d = 0

Therefore, 13th term = 0

Hence, proved.